Douglas Alexander, the shadow foreign secretary, is warning Labour it has only created a bridgehead towards establishing economic credibility and will need to talk "a lot more" about bringing the deficit down if it is to reap political dividends from the government's economic failure.

Making a rare intervention in the debate on Labour's economic approach, he said in a Guardian interview: "I don't think the public has yet heard us talking enough about dealing with the deficit, as well as talking about the need to boost growth and jobs."

He also warned the Scottish first minister, Alex Salmond, that he will endanger the patience of Scotland if he is seen to be trying to fix a referendum on independence.

Alexander added that Labour would support a cap on household welfare benefits, saying: "This is a difficult but necessary step but let us be clear we support the principle, of a benefit cap, but with the important caveat that it should not render people homeless."

Regarded as one of the party's key strategists, Alexander's intervention is likely to be taken as a sign of determination within the shadow cabinet not to lose the momentum created by the two big speeches by leader Ed Miliband and Ed Balls, the shadow chancellor, insisting Labour needed to adjust to an era of austerity, including the need for further spending cuts after the 2015 election.

Balls committed the party to a continued public sector pay freeze, so long as extra help is given to the low paid, a move that prompted a furious union response and was described by Miliband as a watershed for his leadership.

Some critics have accused Miliband of running up the white flag on economic policy, and others that the message is still confused. Alexander believes the party now has to go further to convince the electorate of its credentials, and suggests it has to rebalance its rhetorical emphasis from stimulus to deficit.

He said: "There have always been two parts to the Labour argument – a short-term stimulus now to get the economy moving and medium-term cuts to get the deficit down.

"It was always vital that we won the first part of that argument – that the government are going too far and too fast – and I think thanks to Ed Miliband and Ed Balls we are winning that argument.

"But the second half of that argument – that the deficit has to come down – has to be emphasised more, and all of us have a responsibility to make that case. We have talked a lot about the first and we need to talk a lot more about the second"

He added: "We must convince the public of our commitment to both parts of our argument – securing growth and securing deficit reduction. We have to be heard on both sides of our argument to win."

He also praised Balls's announcement on keeping the public sector pay freeze as the best way to keep people in work. "Ed's was just the first tough choice of many – credibility will involve other tough choices. We cannot promise now to reverse every Tory cut, not least because we do not know the state of public finances in 2015.

"To some that may seem controversial, to me it is common sense. Securing economic credibility is never easy, but it is always essential – fiscal realism is the only path to power."

Urging his party not to back away, he said: "We need to step into this conversation and not step away from it. This is not about positioning against the unions or even towards the electorate. It is more fundamental than that - it is about being open about the condition of the economy. For me fiscal realism is not a betrayal of Labour values, it is the foundation by which we win the trust of the public."

Alexander also urged his party to recognise that the public are in the mood to hear realism from politicians, rather than evasions. "My sense is that, given people's real worries about the economy, there is a yearning for politicians to level with the public. They want us to be honest about the difficult decisions we face to ensure that Britain earns its living and pays its way in the world in the tough years ahead."

Faced by the warnings of disaffiliation by some unions in response to the leadership's shift, Alexander said: "Labour has to hold its nerve. Some of our own supporters will be upset, but we cannot have a reverse gear on this. This is just the start of a difficult process – the two speeches were a beachhead."

He also warned his party that the public would not regard Labour as credible simply if Conservative austerity economics turned out to have failed. Such a view, he said, would be wrong and complacent.

With Labour level pegging with the Tories in the polls he says: "At the time of the Autumn statement we saw that economic failure for the Tories did not translate into political success for us. The task for all of us is to ensure that George Osborne's economic failure becomes an electoral failure for him as well . We will not win the next election just because George Osborne is being exposed as making the wrong economic judgements. The Tory economic policy is clear and it is clearly wrong – you cannot simply cut your way to recovery".

But Alexander argued that the party was paying the price for a deeper failure to be straight with the electorate before the 2010 election, saying: "We should have been much clearer much sooner after the crisis in 2008 about the consequences."

That failure created a benign political environment for the Conservatives. He said: "From 2007 to 2011, the Conservatives worked very hard to establish a public language and a public logic that the crisis was caused by Labour's actions in government. Both Ed Balls and Ed Miliband made important steps forward in correcting that in recent speeches. We all have a responsibility to continue that process."

On Scotland, he said Salmond was trying to avoid a straight choice between separation and the status quo by promoting a third option of greater independence within the UK.

He said: "He is on the horns of a dilemma. He knows he is selling a product that the Scottish people do not want to buy – that is why he is scrambling around trying to find a get out of jail card, and his card is devo max. He cannot explain it, he cannot define it but he hopes it will provide a means by which he can claim victory when he suffers defeat over the sovereignty question.

"As I understand it, Salmond said this week that if 99.5% voted for devo max and 50.1% voted for independence, then Scotland would be independent – try explaining that. If he goes on like this, the tolerance of the public will be strained if this looks like an attempt to rig a referendum. We need a clear and decisive question on independence, and soon.

''The Scottish [Labour] party leader Johann Lamont recently said it is as if he is Moses and he has taken people to the top of the mountain, and shown them the promised land, and then said why don't we camp here for two years."